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Exercises 93
probability that the market research will indicate high sales and
sales will turn out to be high?
(9) An engineer at a chemical plant wishes to assess the probability of
a major catastrophe occurring at the plant during the overhaul of a
processor as a result of a malfunction in the equipment being used
in the overhaul. He estimates that the probability of a malfunction
occurring is 0.1. If this happens there is only a 0.001 probability that
a safety device will fail to switch off the equipment. If the safety
device fails the probability of a major catastrophe is estimated to
be 0.8. What is the probability that a major catastrophe will occur
at the plant during the overhaul as a result of the equipment
malfunctioning?
(10) The probability of the Dow-Jones index rising on the first day of
trading next week is thought to be 0.6. If it does rise then the
probability that the value of shares in a publishing company will
rise is 0.8. If the index does not rise then the publishing company’s
shares will only have a 0.3 probability of rising. What is the
probability that the publishing company’s shares will rise in value
on the first day of trading next week?
(11) A company has two warehouses to sell, one in the town of Kingstones
and another in the nearby suburb of Eadleton. Because there
have been some indications that property prices are likely to rise
over the next six months some of the managers of the company
are urging that the sale should be delayed. It is thought that the
probability of the Kingstones warehouse rising in value by at least
10% is 0.6. If it does rise in value by this amount then there is a 0.9
probability that the Eadleton property will also rise in value by at
least 10%. However, if the Kingstones property rises in value by less
than 10% there is only a 0.3 probability that the Eadleton warehouse
will increase its value by at least 10%. What is the probability that
(a) both warehouses; (b) only one warehouse will increase in value
by at least 10% over the six-month period?
(12) A car owners’ club which offers a rescue service for stranded
motorists has to make a decision on the number of breakdown
patrols to deploy between midnight and 8 a.m. on weekdays during
the summer. The number of requests for assistance received by a
local office during these hours follows the probability distribution
shown below.
No.ofrequests received 0 1 2 3 4 5
Probability 0.01 0.12 0.25 0.42 0.12 0.08